Resistance measurement of all ranges resistances

Electrical and electronics measurement

1. Dr. Sk Babar Ali
Associate Professor
Department of ECE
Aliah University, New Town, Kolkata

2. Measurement of resistance
Propertiesofresistancesplayanimportantroleindeterminingperformance
specificationsforvariouscircuitelementsincludingcoils,windings,insulations,etc.
Itisimportantinmanycasestohavereasonablyaccurateinformationofthemagnitude
ofresistancepresentinthecircuitforanalyzingitsbehavior.Measurementofresistanceis
thusoneoftheverybasicrequirementsinmanyworkingcircuits,machines,transformers,
andmeters.
Apartfromtheseapplications,resistorsareusedasstandardsforthemeasurementof
otherunknownresistancesandforthedeterminationofunknowninductanceand
capacitance.
Fromthepointofviewofmeasurement,resistancescanbeclassifiedas:
LowResistances:Allresistancesoftheorderlessthan1Ωmaybeclassifiedaslow
resistances.
MediumResistances:Resistancesintherange1Ωto100kΩmaybeclassifiedas
mediumresistances.
HighResistances:Resistanceshigherthan100kΩareclassifiedashighresistances.

3. MEASUREMENT OF MEDIUM RESISTANCES
Thedifferentmethodsformeasurementofmediumrangeresistancesare
(i)Ohmmetermethod,
(ii)Voltmeter–ammetermethod,
(iii)Wheatstonebridgemethod.
OhmmeterMethodforMeasuringResistance
series ohmmeter

4. Theseries-typeohmmeterconsistsbasicallyofasensitivedcmeasuringPMMC
ammeterconnectedinparallelwithavariableshuntR2.
ThisparallelcircuitisconnectedinserieswithacurrentlimitingresistanceR1anda
batteryofemfE.
Theentirearrangementisconnectedtoapairofterminals(A–B)towhichtheunknown
resistanceRxtobemeasuredisconnected.
Beforeactualreadingsaretaken,theterminalsA–Bmustbeshortedtogether.Atthis
positionwithRx=0,maximumcurrentflowsthroughthemeter.Theshuntresistance
R2isadjustedsothatthemeterdeflectscorrespondingtoitsrightmostfullscale
deflection(FSD)position.TheFSDpositionofthepointerismarked‘zero-resistance’,
i.e.,0Ωonthescale.
Ontheotherhand,whentheterminalsA–Barekeptopen(Rx→∞),nocurrentflows
throughthemeterandthepointercorrespondstotheleftmostzerocurrentpositionon
thescale.Thispositionofthepointerismarkedas‘∞Ω’onthescale.
Thus,themeterwillreadinfiniteresistanceatzerocurrentpositionandzeroresistance
atfull-scalecurrentposition.Seriesohmmetersthushave‘0’markattheextremeright
and‘∞’markattheextremeleftofscale(oppositetothoseforammetersand
voltmeters).
Themaindifficultyisthefactthatohmmetersareusuallypoweredbybatteries,andthe
batteryvoltagegraduallychangeswithuseandage.TheshuntresistanceR2isusedin
suchcasestocounteractthiseffectandensureproperzerosettingatalltimes.Forzero
setting,Rx=0,whereRm=internalresistanceofthebasicPMMCmetercoil.

5. ThecurrentI2canbeadjustedbyvaryingR2sothatthemetercurrentImcanbeheldatits
calibratedvaluewhenthemaincurrentI1changesduetodropinthebatteryemfE.
DesignofR1andR2:
Meter current Imat full scale deflection (= IFSD.)
• Meter coil resistance, Rm
• Ohmmeter battery voltage, E
• Value of the unknown resistance at half-scale deflection, (Rh), i.e., the value of Rx
when the pointer is at the middle of scale
With terminals A–B shorted, when Rx = 0
Meter carries maximum current, and current flowing out of the battery is given as

6. For full-scale deflection:

7. Shunt-type Ohmmeter
WhentheterminalsA–Bareshorted(Rx=0),themetercurrentiszero,sinceallthecurrentin
thecircuitpassesthroughtheshortcircuitedpathA–B,ratherthanthemeter.Thispositionof
thepointerismarked‘zero-resistance’,i.e.,‘0Ω’onthescale.Ontheotherhand,whenRxis
removed,i.e.,theterminalsA–Bopencircuited(Rx→∞),entirecurrentflowsthroughthe
meter.SelectingpropervalueofR1,thismaximumcurrentpositionofthepointercanbemade
toreadfullscaleofthemeter.Thispositionofthepointerismarkedas‘∞Ω’onthescale.Shunt
typeohmmeters,accordingly,has‘0Ω’attheleftmostpositioncorrespondingtozerocurrent,
and‘∞Ω’attherightmostendofthescalecorrespondingtoFSDcurrent.

9. Wheatstone Bridge for Measuring Resistance
TheWheatstonebridgeisthemostcommonlyused
circuitformeasurementofmediumrange
resistances.TheWheatstonebridgeconsistsoffour
resistancearms,togetherwithabattery(voltage
source)andagalvanometer(nulldetector).
Inthebridgecircuit,R3andR4aretwofixed
knownresistances,R2isaknownvariable
resistanceandRXistheunknownresistancetobe
measured.Underoperatingconditions,currentID
throughthegalvanometerwilldependonthe
differenceinpotentialbetweennodesBandC.A
bridgebalanceconditionisachievedbyvaryingthe
resistanceR2andcheckingwhetherthe
galvanometerpointerisrestingatitszeroposition.
Atbalance,nocurrentflowsthroughthe
galvanometer.Thismeansthatatbalance,
potentialsatnodesBandCareequal.

10. Inotherwords,atbalancethefollowingconditionsaresatisfied:
1.Thedetectorcurrentiszero,i.e.,1D=0andthusIt=I3andI2=I4
2.PotentialsatnodeBandCaresame,i.e.,VB=VC,orinotherwords,voltagedrop
inthearmABequalsthevoltagedropacrossthearmAC,i.e.,VAB=VACandvoltage
dropinthearmBDequalsthevoltagedropacrossthearmCD,i.e.,VBD=VCD
FromtherelationVAB=VACwehaveI1×Rx=I2×R2(1)
Atbalanced‘null’position,sincethegalvanometercarriesnocurrent,itasifactsasif
opencircuited,thus
Thus,measurementoftheunknownresistance
ismadeintermsofthreeknownresistances.
ThearmsBDandCDcontainingthefixed
resistancesR3andR4arecalledtheratioarms.
ThearmACcontainingtheknownvariable
resistanceR2iscalledthestandardarm.The
rangeoftheresistancevaluethatcanbe
measuredbythebridgecanbeincreasedsimply
byincreasingtheratioR3/R4.

11. Errors in a Wheatstone Bridge
AWheatstonebridgeisafairlyconvenientandaccuratemethodformeasuringresistance.
However,itisnotfreefromerrorsaslistedbelow:
1.Discrepanciesbetweenthetrueandmarkedvaluesofresistancesofthethreeknownarmscan
introduceerrorsinmeasurement.
2.Inaccuracyofthebalancepointduetoinsufficientsensitivityofthegalvanometermayresultin
falsenullpoints.
3.Bridgeresistancesmaychangeduetoself-heating(I2R)resultinginerrorinmeasurement
calculations.
4.Thermalemfsgeneratedinthebridgecircuitorinthegalvanometerintheconnectionpointsmay
leadtoerrorinmeasurement.
5.Errorsmaycreepintomeasurementduetoresistancesofleadsandcontacts.Thiseffectishowever,
negligibleunlesstheunknownresistanceisofverylowvalue.
6.Theremayalsobepersonalerrorsinfindingthepropernullpoint,takingreadings,orduring
calculations.
Errorsduetoinaccuraciesinvaluesofstandardresistorsandinsufficientsensitivityof
galvanometercanbeeliminatedbyusinggoodqualityresistorsandgalvanometer.
Temperaturedependentchangeofresistanceduetoself-heatingcanbeminimizedbyperforming
themeasurementwithinasshorttimeaspossible.
Thermalemfsinthebridgearmsmaycauseserioustrouble,particularlywhilemeasuringlow
resistances.Thermalemfingalvanometercircuitmaybeseriousinsomecases,socaremustbetaken
tominimizethoseeffectsforprecisionmeasurements.Somesensitivegalvanometersemployall-
coppersystems.
Theeffectofthermalemfcanbebalancedoutinpracticebyaddingareversingswitchinthecircuit
betweenthebatteryandthebridge,thenmakingthebridgebalanceforeachpolarityandaveraging
thetworesults.

12. FourarmsofaWheatstonebridgeareasfollows:AB=100Ω,BC=10Ω,CD=4Ω,
DA=50Ω.Agalvanometerwithinternalresistanceof20ΩisconnectedbetweenBD,
whileabatteryof10-VdcisconnectedbetweenAC.Findthecurrentthroughthe
galvanometer.FindthevalueoftheresistancetobeputonthearmDAsothatthebridge
isbalanced.
Example
SolutionConfigurationofthebridgewiththe
valuesgivenintheexampleisasshownbelow:
Tofindoutcurrentthroughthegalvanometer,it
isrequiredtofindoutTheveninequivalent
voltageacrossnodesBDandalsotheThevenin
equivalentresistancebetweenterminalsBD.
TofindoutThevenin’sequivalentvoltageacross
BD,thegalvanometerisopencircuited.
Atthiscondition,voltagedropacrossthearmBC
isgivenby

13. Hence,voltagedifferencebetweenthenodesBandD,ortheTheveninequivalentvoltage
betweennodesBandDisVTH=VBD=VB–VD=VBC–VDC=0.91-0.74=0.17V
ToobtaintheTheveninequivalentresistancebetweennodesBandD,the10Vsource
needtobeshorted,andthecircuitlookslikethefiguregivenbelow.

14. Kelvin’s Double-Bridge Method for Measuring Low Resistance
Kelvin’sdouble-bridgemethodisoneofthebestavailablemethodsformeasurementof
lowresistances.ItisactuallyamodificationoftheWheatstonebridgeinwhichtheerrors
duetocontactsandleadresistancescanbeeliminated.
Kelvin’s double bridge
incorporatestheideaofasecond
setofratioarms,namely,pand
q,andhencethename‘double
bridge’.Xistheunknownlow
resistancetobemeasured,andS
isaknownvaluestandardlow
resistance.‘r’isaverylow
resistanceconnectingleadused
connecttheunknownresistance
XtothestandardresistanceS.
AllotherresistancesP,Q,p,and
qareofmediumrange.Balance
inthebridgeisachievedby
adjustingS.

15. Underbalancedcondition,potentialsatthenodesaandbmustbeequalinorderthatthe
galvanometerGgives“null”deflection.Sinceatbalance,nocurrentflowsthroughthe
galvanometer,itcanbeconsideredtobeopencircuitedandthecircuitcanberepresented
as

19. Example:A4-terminalresistorwasmeasuredwiththehelpofaKelvin’sdouble
bridgehavingthefollowingcomponents:Standardresistor=98.02nW,innerratio
arms=98.022Ωand202W,outerratioarms=98.025Ωand201.96W,resistanceof
thelinkconnectingthestandardresistanceandtheunknownresistance=600nW.
Calculatethevalueoftheunknownresistance.

20. Megohmmeter, or Meggar, for High Resistance Measurement
Oneofthemostpopularportabletypeinsulationresistancemeasuringinstrumentsisthe
megohmmeterorinshort,meggar.Themeggarisusedverycommonlyformeasurement
ofinsulationresistanceofelectricalmachines,insulators,bushings,etc.
Thetraditionalanalogdeflecting-typemeggarisessentiallyapermanentmagnetcrossed-
coilshunttypeohmmeter.
Theinstrumenthasasmallpermanentmagnetdcgeneratordeveloping500Vdc(some
othermodelsalsohave100V,250V,1000or2500Vgenerators).Thegeneratorishand
driven,throughgeararrangements,andthroughacentrifugallycontrolledclutchswitch
whichslipsatapredefinedspeedsothataconstantvoltagecanbedeveloped.Some
meggarsalsohaverectifiedacaspowersupply.

21. Themovingsysteminsuchinstrumentsconsistsoftwocoils,thecontrolcoilCCandthe
deflectingcoilCD.Boththecoilsaremountedrigidlyonashaftthatcarriesthepointeras
well.Thetwocoilsmoveintheairgapofapermanentmagnet.Thetwocoilsarearranged
withsuchnumbersofturns,radiiofaction,andconnectedacrossthegeneratorwithsuch
polaritiesthat,forexternalmagneticfieldsofuniformintensity,thetorqueproducedbythe
individualcoilsareinoppositionthusgivinganastaticcombination.
ThedeflectingcoilisconnectedinserieswiththeunknownresistanceRXunder
measurement,afixedresistorRDandthenthegenerator.
Thecurrentcoilorthecompensatingcoil,alongwiththefixedresistanceRCisconnected
directlyacrossthegenerator.Foranyvalueoftheunknown,thecoilsandthepointertakeup
afinalsteadypositionsuchthatthetorquesofthetwocoilsareequalandbalancedagainst
eachother.
Forexample,whentheresistanceRXundermeasurementisremoved,i.e.,thetestterminals
areopen-circuited,nocurrentflowsthroughthedeflectingcoilCD,butmaximumcurrentwill
flowthroughthecontrolcoilCC.ThecontrolcoilCCthussetsitselfperpendiculartothe
magneticaxiswiththepointerindicating‘∞Ω’asmarkedinthescale.
AsthevalueofRXisbroughtdownfromopencircuitcondition,moreandmorecurrent
flowsthroughthedeflectingcoilCD,andthepointermovesawayfromthe‘∞Ω’mark
clockwiseonthescale,andultimatelyreachesthe‘0Ω’markwhenthetwotestterminalsare
shortcircuited.
Thesurfaceleakageproblemistakencareofbytheguard-wirearrangement.Theguardring
GRandtheguardwiredivertsthesurfaceleakagecurrentfromreachingthemainmoving
systemandinterferingwithitsperformance.